DescriptionEmerging applications of short-range communication such as the Internet of Things and body area networks highlight the importance of processing energy, as compared to transmit energy. In this thesis, we investigate fundamental limits of reliable communication when receiver processing is powered by random energy sources and subject to constraints on energy storage. We propose a receiver model that captures the trade-off between sampling energy and decoding energy. The model relies on the decoding energy being a decreasing function of the capacity gap between the code rate and the channel capacity. The receiver can save energy in sampling by dropping a fraction of samples, at the cost of reducing the effective capacity and thus increasing the energy needed for decoding. While sampling and decoding energies are typically comparable, the key issue is that the sampling is a real-time process; the samples must be collected during the transmission time of that packet. Thus the energy harvesting rate and battery size may constrain the sampling rate. This model allows us to characterize the maximum throughput of a basic communication channel with limited processing energy. This is done based on striking the balance between the sampling and decoding energy, subject to limited random arrival of energy, and limited battery size. We further extend this result to multi-user scenarios, where multiple transmitters communicate with a single receiver with limited energy. We introduce the concept of receive multi-user diversity, in which the receiver decodes the messages experiencing the strongest channels in order to reduce the decoding energy per user. Next, we propose using hybrid automatic retransmission request (HARQ) with soft combining to reduce the processing energy and improve the throughput under limited receiver energy. In this protocol, the receiver keeps requesting additional redundancy in order to increase the capacity gap, which in turn reduces the processing energy. We compare the performance of incremental redundancy (IR) HARQ, and Repetition-HARQ. In these systems, the decoding energy is a decreasing function of the capacity gap but an increasing function of the code-length. The IR-HARQ protocol yields a better capacity gap, but increases the code-length, while Repetition-HARQ offers less improvement in the capacity gap, but does not increase the effective code-length. Thus, contrary to systems without receiver energy constraints in which IR-HARQ always performs better, here, depending on the system parameters, Repetition-HARQ can outperform IR-HARQ. Finally, we study energy efficiency and energy harvesting in LTE networks. We formulate a single-cell downlink scheduling problem that enforces constraints on the selection of transmission parameters. Linear cost constraints on the set of channels are also imposed in order to accommodate energy efficiency considerations. We show that the resulting problem is NP-hard and we propose a deterministic multiplicative- update algorithm for which we establish an approximation guarantee. We also consider the problem of downlink scheduling in an LTE network powered by energy harvesting devices. We formulate optimization problems that seek to maximize two popular energy efficiency metrics subject to LTE network constraints and energy harvesting causality constraints. We focus on a key sub-problem and show that this problem is NP-hard. Then we reformulate it as a constrained submodular set function maximization problem which can be solved with a constant-factor approximation using a greedy algorithm.